منابع مشابه
A Generalized Cantor Theorem
A well known theorem of Cantor asserts that the cardinal of the power-set of a given set always exceeds the cardinal of the original set. An analogous result for sets having additional structure is the well known theorem that the set of initial segments of a well ordered set always has order type greater than the original set. These two theorems suggest that there should be a similar result for...
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This paper is a continuation of a previous author’s article; the result is now extended to the case when the lattice under consideration need not have the least element.
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If {qn} is a lacunary sequence of integers, and if for each n, cn(x) and c-n(x) are trigonometric polynomials of degree n, then {Cn(X)} must tend to zero for almost every x whenever {cn(x)ei?nX + c-n(-x)e-i?'nX} does. We conjecture that a similar result ought to hold even when the sequence {f On} has much slower growth. However, there is a sequence of integers {nj } and trigonometric polynomial...
متن کاملA Cantor-Bernstein Theorem for Paths in Graphs
As every vertex of this graph has one “outgoing” and at most one “incoming” edge, each of those components is a cycle or an infinite path. In each of these paths and cycles we now select every other edge to mark the desired bijection. The Cantor-Bernstein problem, rephrased as above for graphs, has a natural generalization to paths. Let G be any graph, and let A and B be disjoint sets of vertic...
متن کاملCantor-Bernstein theorem for pseudo BCK-algebras
For any σ-complete Boolean algebras A and B, if A is isomorphic to [0, b] ⊆ B and B is isomorphic to [0, a] ⊆ A, then A B. Recently, several generalizations of this known CantorBernstein type theorem for MV-algebras, (pseudo) effect algebras and `-groups have appeared in [1], [2], [4] and [5]. We prove an analogous result for certain pseudo BCK-algebras—a noncommutative extension of BCK-algebra...
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ژورنال
عنوان ژورنال: The Mathematical Intelligencer
سال: 2011
ISSN: 0343-6993,1866-7414
DOI: 10.1007/s00283-011-9242-3